The invention concerns a method for determination of roll density, in which method the density of the web to be wound is determined in connection with the web reel and which method uses the known relation between the length, diameter, basis weight and density of the web to be wound       l    =                  πρ        ⁡                  (                                    D              2                        -                          D              0              2                                )                            4        ⁢        b              ,                l=length of web to be wound        π=3.1415926 . . .        ρ=density        D=diameter        Do=diameter of winding core        b=basis weight        
A calculation formula is known in the state of the art, which can be used e.g. to determine the ply thickness of the wound web or to measure the roll density.
The publication Roisum, D. R. “The Measurement of Web Stresses during Roll Winding”, Oklahoma State University, 1990, s. 140-141 presents a formula in connection with measurement of roll density:       ρ    =                  4        ⁢                  b          ⁡                      (            length            )                                      π        ⁡                  (                                    d              i              2                        -                          d                              i                -                1                            2                                )                      ,                ρ=average web density over the measured distance        π=3.1415926 . . .        length=cumulated web length over the measured distance        di=roll diameter on measurement occasion i        b=basis weight of web        
The formula was used in FI patent application 780893 for calculation of the thickness of a paper web:   d  =                    R        k            -              R                  k          -          1                                    n        k            -              n                  k          -          1                     d(Lk−Lk−1)=π(Rk2−Rk−12),                d=average web thickness over the measuring distance        Rk=roll radius on measurement occasion k        Lk=web length on measurement occasion k        π=3.1415926 . . .        nk=cumulative number of plies        
A similar formula is also presented in the publication Happonen, E. “Paperirullan Rullaustiheyden Mittauslaitteisto” (“Equipment for Measuring the Winding Density of a Paper Roll” Diploma Work), Diplomityö, Teknillinen Korkeakoulh (University of Technology), 1985 p. 17, which presents a calculation formula for the average thickness of wound paper in connection with the measurement of the thickness of wound paper over a certain winding distance Dk=(Rk−Rk−1)/(nk−nk−1).
However, it has proved problematic in the determination of web density or thickness to eliminate the inexactness resulting in measurement results from noise and from other disturbances.
As is known in the state of the art, the formula has not been used generally, because the density measurement according to the formula has been prevented by the inexact diameter measurement and by the attending vibration frequency of the roll center. This is especially problematic when measurement of the location of the roll center is used in the diameter measurement.
As regards the state of the art, reference is also made to DE patent publication 41 28 706, which presents a method for determination of roll tightness when winding a material web on a winding machine, where the thickness of wound plies is found out for the roll tightness and wherein the length of the wound web affecting the diameter is measured directly. In the method, the roll diameter is measured directly by degrees as a transition of the roll center and then the ply thickness is calculated using a formula similar to the one described above       S    =                            (                                    D              2              2                        -                          D              1              2                                )                ⁢        π                    4        ⁢        Δ        ⁢                                   ⁢        l              ,                S=average web thickness over the measuring distance        D1=roll diameter in the beginning of the measuring distance        D2=roll diameter at the end of the measuring distance        π=3.1415926 . . .        Δl=web length cumulated over the measuring distance        
In the calculation, high-frequency disturbances caused in the diameter measurement by vibration of the roll center are eliminated by low-pass filtration. In this known solution the filtration is thus based on the assumption that disturbances are of a high frequency and the filtration will thus be fairly rough.
The use of low-pass filtration to reduce the share of the noise of the measurement signal is based on the assumption that the noise summed on the measurement is of zero average value, that is, unbiased, and that its frequency content differs from the measurement signal proper. The filter removes from the measurement those higher frequencies, which the noise brings along, whereby the desired original measurement signal will remain. This may cause inexactness, since also a part of the desired measurement signal is filtered and also a part of the noise will remain. In addition, phase lag, that is, delay, may result in the measurement signal.
If low-pass filtration were to be used in order to achieve an efficient filtration at all machine ruling speeds and with all roll diameters, then the boundary frequency of low-pass filtration ought to be changed constantly as these factors are changing. Since the main reason for measurement noise is the waving in diameter measurement caused by the eccentricity of the roll center, the frequency content of measurement noise is strongly dependent on the rotation frequency of the roll, which again depends on the running speed and on the roll diameter, being typically at a maximum a little while after winding has begun. It is a problem with the state-of-the-art procedure that it is not easy in practice to implement a constant changing during operation of the boundary frequency of any higher rate low-pass filter.
Various ways of measuring the roll diameter are known in the state of the art, the most widely used being pulse measurement, wherein pulse measurement is used for measuring the roll circumference. The diameter information obtained through pulse measurement has been used in order to find out the web thickness. When one ply is completed on the roll, the length measure is taken-from the carrying roller and the paper thickness is obtained by finding out how quickly the roll diameter increases. It is problematic to determine the web thickness exactly, because when winding large-diameter rolls wherein the web is thin, differences in orders of magnitude have caused inexactness.
The roll hardness determines how tightly the roll is wound. This corresponds with a certain internal compression pressure distribution between the plies, which is the higher the tighter the roll. In addition, roll hardness depends on the hardness of the paper itself, that is, on the elastic modulus in the Z direction, which is different for different paper grades, that is, rolls of various kinds wound to the same tightness may have a different hardness. Roll density correlates with tightness or hardness, because an increased compression pressure will cause a deformation that will compress the paper layers together.